The conventional design of teeth shape for shifting a chain from a smaller sprocket wheel to a larger sprocket wheel of the multi-stage sprocket assembly is based on a supposition that the linear distance between the center of the escape roller and that of the engaging roller is an integer multiple of the chain pitch during gear shifting process, i.e., the chain portion between the aforesaid two rollers is aligned straight, such as U.S. Pat. Nos. 4,889,521 and 4,268,259. The tooth shapes of the sprocket wheels are trimmed in accordance with the aforesaid supposition.
During the gear shifting process from a smaller sprocket wheel to a larger sprocket wheel, the chain will first contact with the side surface of the larger sprocket wheel before fully engagement occurred. Due to the aforesaid contact, there will be an articular angle induced between the first contact link and the roller that actually first engage with the tooth of the larger sprocket. That means, the chain between the escape roller and the engaging roller is not aligned straight, therefore, the linear distance between the roller centers would not be an integer multiple of the chain pitch. Consequently, the supposition of the engaging operation in the conventional shifting design is not consistent with the actual operation.